The Michelson Doppler Imager experiment on SOHO has revealed a "magnetic carpet" dominated by the emergence of bipolar magnetic flux in ephemeral active regions, which subsequently split into small flux elements that drift into the magnetic network. The effects of granular and supergranular convection on these flux elements are represented here by kinematic modeling: Elementary flux tubes are transported passively by the supergranular flow, while experiencing small random displacements produced by granulation. They end up in the magnetic network that surrounds the supergranules, where they eventually meet oppositely directed fields and are annihilated. The model calculations show that the total unsigned magnetic flux will decay within a few days unless it is continually replenished. A statistically steady state with a total unsigned flux of 2-3 × 1023?Mx over the whole solar surface can be maintained if bipolar flux emerges at a rate of 7 × 1022?Mx?day-1, as indicated by published measurements of the rate at which ephemeral active regions appear.
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